This is a picture of the problem that i struggled on during the Unit 1 (Measurement, Atomic structure and Periodic table) Test. After finishing the first page of the test this problem came up, and honestly i didn't review for the test so my mind just completely went blank. The only thing i remembered in class for solving the percentage was the x and 1-x but this seemed to make no sense to me. I wrote this down on the test, and plugged some numbers in, but decided to restart, confused to what the variable and number meant. I continuously pondered over this question, in the end, my efforts were futile. I moved on with the test. After completing the test i went back to the problem, with a lot of time left, i pondered more. I began to ask myself about how i would find the average atomic mass. With my sleep deprived mind that day, i had an eureka, the problem was so simple, i just had to work backwards. It was just simple algebra. Since to find the average atomic mass of an element is (percent of abundance/100)( x atom amu) + whatever isotopes are left which would lead to the average atomic mass. This made me think about the x and 1-x a bit more. I wrote down the equation 19.99 (100-x) + 21.99 (x/100)=20.18amu. Since x is abundance of one isotope, 100-x must be the remaining difference which would be the other isotopes abundance. And i thought about x and 1-x, it was similar but it calculated percent directly without the need of moving decimal places back in the solution. Upon the happening of this spectacular moment, i raced through the problem and figured out the answers. Even after finishing the problem i did not trust the work i had done so i plugged the values back in to make sure it all made perfect sense. Now that i think back on it, in the beginning i didn't know what to do at all, but later it was through persistence and questioning that helped me figure out the problem. I actually felt very proud even though now i realize it was easy as pie.
This is a picture of the problem that i struggled on during the Unit 1 (Measurement, Atomic structure and Periodic table) Test. After finishing the first page of the test this problem came up, and honestly i didn't review for the test so my mind just completely went blank. The only thing i remembered in class for solving the percentage was the x and 1-x but this seemed to make no sense to me. I wrote this down on the test, and plugged some numbers in, but decided to restart, confused to what the variable and number meant. I continuously pondered over this question, in the end, my efforts were futile. I moved on with the test. After completing the test i went back to the problem, with a lot of time left, i pondered more. I began to ask myself about how i would find the average atomic mass. With my sleep deprived mind that day, i had an eureka, the problem was so simple, i just had to work backwards. It was just simple algebra. Since to find the average atomic mass of an element is (percent of abundance/100)( x atom amu) + whatever isotopes are left which would lead to the average atomic mass. This made me think about the x and 1-x a bit more. I wrote down the equation 19.99 (100-x) + 21.99 (x/100)=20.18amu. Since x is abundance of one isotope, 100-x must be the remaining difference which would be the other isotopes abundance. And i thought about x and 1-x, it was similar but it calculated percent directly without the need of moving decimal places back in the solution. Upon the happening of this spectacular moment, i raced through the problem and figured out the answers. Even after finishing the problem i did not trust the work i had done so i plugged the values back in to make sure it all made perfect sense. Now that i think back on it, in the beginning i didn't know what to do at all, but later it was through persistence and questioning that helped me figure out the problem. I actually felt very proud even though now i realize it was easy as pie.